Details

Time bar (total: 4.8s)

sample49.0ms

Algorithm
intervals
Results
27.0ms393×body80valid
6.0ms135×body80nan

simplify101.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0247
1535
21065
32695
49045
539765
650015

prune12.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 1.9b

Counts
2 → 2

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (+ 1.0 (* 10.0 k)) (* k k))
1.9b
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
12×add-exp-log
7×add-cbrt-cube add-log-exp
5×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×div-exp
3×fma-def times-frac prod-exp associate-/r* sum-log
2×pow1 cbrt-undiv expm1-log1p-u flip3-+ associate-/r/ flip-+ log1p-expm1-u
1×+-commutative pow-to-exp associate-+l+ frac-2neg pow-exp clear-num cbrt-unprod div-inv associate-/l*
Counts
2 → 45
Calls
2 calls:
5.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
8.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series140.0ms

Counts
2 → 6
Calls
2 calls:
18.0ms
(+ (+ 1.0 (* 10.0 k)) (* k k))
123.0ms
(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify43.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0363456
11675385
25001363

prune127.0ms

Filtered
51 candidates to 39 candidates (76.5%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New49251
Fresh101
Picked011
Done000
Total50353

Merged error: 0.0b

Counts
53 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma k 10.0 1.0)
0.1b
(/ (pow k m) (/ (fma k k (fma k 10.0 1.0)) a))
4.7b
(/ (fma k k (fma k 10.0 1.0)) a)
14.9b
(cbrt (pow (/ (pow k m) (/ (fma k k (fma k 10.0 1.0)) a)) 3))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
480×times-frac
249×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
216×unpow-prod-down
198×cbrt-prod
96×cube-prod
41×sqr-pow
26×div-inv
19×add-exp-log
16×associate-/r*
11×add-cbrt-cube
10×div-exp associate-/l*
4×pow1 cbrt-undiv expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/r/
2×pow-to-exp frac-2neg pow-exp clear-num
1×cube-div cube-mult cbrt-div pow1/3 unpow3 rem-cbrt-cube fma-udef
Counts
4 → 381
Calls
4 calls:
1.0ms
(fma k 10.0 1.0)
8.0ms
(/ (pow k m) (/ (fma k k (fma k 10.0 1.0)) a))
3.0ms
(/ (fma k k (fma k 10.0 1.0)) a)
22.0ms
(cbrt (pow (/ (pow k m) (/ (fma k k (fma k 10.0 1.0)) a)) 3))

series331.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(fma k 10.0 1.0)
125.0ms
(/ (pow k m) (/ (fma k k (fma k 10.0 1.0)) a))
43.0ms
(/ (fma k k (fma k 10.0 1.0)) a)
132.0ms
(cbrt (pow (/ (pow k m) (/ (fma k k (fma k 10.0 1.0)) a)) 3))

simplify98.0ms

Algorithm
egg-herbie
Counts
393 → 393
Iterations

Useful iterations: 1 (36.0ms)

IterNodesCost
020854746
150014709

prune808.0ms

Filtered
393 candidates to 228 candidates (58.0%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New3930393
Fresh011
Picked011
Done011
Total3933396

Merged error: 0.0b

Counts
396 → 3

localize23.0ms

Local error

Found 4 expressions with local error:

1.5b
(fma (/ (exp (* -1 (* m (log (/ 1 k))))) k) (/ a k) (- (* 99.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))) (* 10.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3)))))
6.8b
(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))
7.2b
(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))
10.7b
(- (* 99.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))) (* 10.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
24×add-exp-log
19×times-frac associate-/r*
14×add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube
12×unpow-prod-down div-exp
8×exp-neg distribute-rgt-neg-out associate-/l/
6×cube-prod associate-*r/ prod-exp add-log-exp
4×pow1 cbrt-undiv expm1-log1p-u pow-to-exp mul-1-neg log-rec pow-exp un-div-inv log1p-expm1-u sqr-pow
2×cube-mult frac-2neg unpow3 clear-num cbrt-unprod div-inv associate-/l*
1×sub-neg flip3-- fma-neg diff-log prod-diff frac-sub flip-- fma-udef
Counts
4 → 115
Calls
4 calls:
1.0ms
(fma (/ (exp (* -1 (* m (log (/ 1 k))))) k) (/ a k) (- (* 99.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))) (* 10.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3)))))
15.0ms
(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))
15.0ms
(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))
20.0ms
(- (* 99.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))) (* 10.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))))

series501.0ms

Counts
4 → 12
Calls
4 calls:
180.0ms
(fma (/ (exp (* -1 (* m (log (/ 1 k))))) k) (/ a k) (- (* 99.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))) (* 10.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3)))))
70.0ms
(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))
83.0ms
(/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))
167.0ms
(- (* 99.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 4))) (* 10.0 (/ (* a (exp (* -1 (* m (log (/ 1 k)))))) (pow k 3))))

simplify104.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 2 (81.0ms)

IterNodesCost
06231864
131711567
250011493

prune690.0ms

Filtered
127 candidates to 92 candidates (72.4%)
Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New1270127
Fresh000
Picked011
Done022
Total1273130

Merged error: 0.0b

Counts
130 → 3

regimes89.0ms

Accuracy

98.1% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 1.9b

bsearch63.0ms

Steps
ItersRangePoint
8
248277588.46065098
9835344464437.621
30891094764.078453

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04834
15434
25434

end0.0ms

sample1.4s

Algorithm
intervals
Results
856.0ms12060×body80valid
190.0ms4221×body80nan